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Bài tập 11 trang 96 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Cho tam giác ABC cân tại A có
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Đề bài

Cho tam giác ABC cân tại A có \(\widehat {BAC} < {60^o}\) a) Chứng minh: \(\widehat {ABC} > {60^o}\) b) Chứng minh: AB > BC và AC > BC.

Lời giải chi tiết

a) ∆ABC cân tại A (gt) \( \Rightarrow \widehat {ABC} = \widehat {ACB}\)∆ABC có \(\widehat {BAC} + \widehat {ABC} + \widehat {ACB} = 180^\circ\)Do đó \(2\widehat {ABC} = 180^\circ  - \widehat {BAC} > 180^\circ  - 60^\circ  = 120^\circ\) (vì \(\widehat {BAC} < 60^\circ\))\( \Rightarrow \widehat {ABC} > 60^\circ\)b) ∆ABC có \(\widehat {ABC} > \widehat {BAC}\) (vì \(\widehat {ABC} > 60^\circ  > \widehat {BAC}\))=> AC > BC (quan hệ giữa góc và cạnh trong một tam giác)Mà AB = AC (∆ABC cân tại A) nên AB > BC.

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